What factors drive resident-healthcare worker networks in long-term healthcare facilities?

An Application of Multilevel Exponential-Family Random Graph Models with Bi-partite Networks

George G. Vega Yon
george.vegayon@utah.edu

Division of Epidemiology

The University of Utah

2024-06-04

Acknowledgements

This is joint work with:

  • Chong Zhang
  • Karim Khade
  • Nelson Chang
  • Lindsay Visnovsky
  • Alun Thomas
  • Candace Haroldsen
  • Kristina Stratford
  • Matthew H. Samore

CDC Prevention Epicenter and MInD Programs support this work.

Preliminaries

Background

  • Over a thousand long-term care facilities [LTCFs] reached infection rates of 75% or more (year 1 of COVID-19) (HHS Office of Inspector General 2023).

  • On average, over 1.7 million patients in the US acquired a Healthcare Associated Infection [HAI]. (Haque et al. 2018).

  • The estimated cost of HAI in the US for 2016 is between 7.2 and 14.9 billion USD. (Forrester, Maggio, and Tennakoon 2022).

  • The spread of pathogens within healthcare facilities is boosted mainly through contact with and movement of healthcare workers [HCW].

  • Little is known about the structure of healthcare worker networks and how they relate to patient characteristics.

Networks in Healthcare

  • Most published work focuses on high-level summaries: overall contact rate, duration of contacts, and network-based measures like transitivity.

  • Analysis of the topology of the contact networks, especially as they relate to resident and HCP factors, has been limited.

  • Most network studies focus on physicians, a handful incorporate other healthcare professionals, and most use projected networks, focusing only on physician-physician networks (DuGoff et al. 2018).

  • Moen et al. (2016) provides a large-scale analysis of patient-physician networks:

    • Use Exponential-Family Random Graph Models [ERGMs] to assess assortativity between different types of healthcare professionals within two hospitals.
    • Used the physician-projected networks (a uni-partite version featuring physicians with ties representing shared patients)
    • This approach discards any signal encoded in bipartite structures.

For other studies, see Champredon et al. (2018), Duval et al. (2018), Vilches et al. (2021), and Schneider et al. (2022).

Data: Overview

  • The data were collected through the CDC Epicenter program in collaboration with CDC Emerging Infections Program (EIP) sites in seven states (CA, GA, MD, MN, NY, TN).

  • Twenty-five LTCFs were enrolled in the study.

  • Data collection occurred in two units: One long-term care unit and one higher acuity care unit at each LTCF over two days.

  • The data used in this study come from interviews conducted at each enrolled facility on each day of data collection.

  • Key to this study: using information about HCW-resident interactions to build bipartite networks.

Image generated using Bing’s AI designer using the prompt: “generate a realistic image of a health care provider giving care to a long-term healthcare facility patient.”

Descriptive stats: Resident and Nursing Home Demographics

Unit Type # of Units # of Residents Mean Length of Stay (Days) Mean Age (Years) Diabetes In-dwelling Devices Receiving Antibiotics (Systemic) Receiving Antibiotics (Topical) MDRO at Time of Visit
Mixed 17 279 985 77 100
(35.8%)		 49
(17.6%)		 16
(5.7%)		 1
(0.4%)		 6
(2.2%)
Long-Term Care 8 1161 1060 77 381
(32.8%)		 154
(13.3%)		 63
(5.4%)		 36
(3.1%)		 50
(4.3%)
Skilled Nursing 11 688 327 74 340
(49.4%)		 145
(21.1%)		 108
(15.7%)		 64
(9.3%)		 30
(4.4%)
Ventilator 4 269 867 60 124
(46.1%)		 269
(100.0%)		 48
(17.8%)		 16
(5.9%)		 73
(27.1%)
Other 7 122 434 79 98
(80.3%)		 25
(20.5%)		 23
(18.9%)		 48
(39.3%)		 4
(3.3%)

NH: Nursing home, MDRO: Multi-Drug Resistant Organisms

Descriptive stats: Intercept Interview Results

Interview
HCP Type Resident Interactions per hour 1 Tasks per hour Tasks per resident per hour
CAN 2.7 6.2 2.3
Nurse 3.4 5.0 1.5
Other 2.5 4.5 1.8
Physician/PA/NP 1.0 0.9 0.9
PT/OT 1.3 1.9 1.5
Resp. Therapy 3.4 5.4 1.6

Data

Figure 1 from Nelson Chang et al. (2023): Distribution of resident care types by health care provider types

Key for this study: using information about HCW-resident interactions to build bipartite networks.

Bipartite Networks

  • In bipartite networks, nodes are divided into two sets, and edges connect only nodes from different sets.

  • Ties represent an interaction between a resident and a healthcare worker.

Figure 1: Example of a resident-health careworker network. The figure shows the bipartite network with residents colored green and healthcare workers colored blue.

Figure 2: The figure shows all 99 networks. Like in Figure Figure 1, healthcare workers are colored blue, while residents are colored green

Methods

ERGMs

What micro-level processes/structures
are we more likely to observe in these networks?

  • Exponential-Family Random Graph Models [ERGMs] are used to model social networks [Robins et al. (2007); Holland and Leinhardt (1981); Frank and Strauss (1986); Wasserman and Pattison (1996); Snijders et al. (2006); and others].

  • An observed graph \bm{y} is characterized by a set of sufficient statistics \bm{g}\left(\bm{y}\right) and parameters \bm{\theta}. In a model that also includes node characteristics X, this leads to the following probability function:

    % {\text{Pr}_{\mathcal{Y},\bm{\theta}}\left(\bm{Y}= \bm{y}\left|\;X\right.\right)}% = \frac{% \text{exp}\left\{{\bm{\theta}}^{\bm{t}}\bm{g}\left(\bm{y}, X\right)\right\}% }{ \kappa\left(\bm{\theta}, X\right) },\quad\forall \bm{y}\in\mathcal{Y} \tag{1}

    Where \kappa_{\mathcal{Y}}\left(\bm{\theta}\right){} = \sum_{\bm{y}\in\mathcal{Y}}\text{exp}\left\{{\theta}^{\bm{t}}\bm{g}\left(\bm{y}, X\right)\right\} is the normalizing constant, and \mathcal{Y} is the support of the model that is usually assumed to include all graphs of the same type (e.g., directed or undirected) and size, that do not include self-ties.

  • We use statnet’s’ ergm.multi R package (Handcock et al. 2018; Krivitsky, Coletti, and Hens 2023a) to study the prevalence of various network structures associated with patient cohorting based on patients’ characteristics

  • We present one of the first applications of pooled bipartite ERGMs.

ERGM terms

We can use ERGMs to question various network structures. Here are some of the terms we tested in our models:

Name Representation
Edge count
\sum_{i<j}y_{ij}
HCW-centered two-star \sum_{i\in H, \{j<k\}\in R}y_{ij}y_{ik}
Resident-centered two-star \sum_{i\in R, \{j<k\}\in H}y_{ji}y_{ki}
HCW-centered homophilic two-star \sum_{i\in H, \{j<k\}\in R}\mathbf{1}\left(x_{j} = x_k\right) y_{ij}y_{ik}
Name Representation
Res.-centered homophilic two-star \sum_{i\in R, \{j<k\}\in H}\mathbf{1}\left(x_{j} = x_k\right)y_{ji}y_{ki}
Dyad-wise one shared residents1 \sum_{\{i<j\}\in H, k\in R}y_{ik}y_{jk}
Dyad-wise two shared residents^1 \sum_{\{i<j\}\in H, \{k<h\}\in R}y_{ik}y_{jk}y_{ih}y_{jh}

ERGM Descriptive statistics

Table 1: Observed statistics for the 93 networks used in the analysis
Total count Average count
Structural terms
Edges 7800 83.87
log(n) \times edges 65005 698.98
GWDSP1 (decay fixed 0.75) 3383 36.38
Nodal effects
Resident under wound care (yes/no) 1752 18.84
Resident is bedridden (yes/no) 899 9.67
Resident mixing (HCW centered)
None with ventilator 45971 494.31
Both with ventilator 1256 13.51
None with diabetes 20278 218.04
Both with diabetes 7444 80.04
HCW mixing (resident centered)
None nurse 3161 33.99
Both nurse 366 3.94
None therapist 6187 66.53
Both therapist 68 0.73

Figure 3: Distribution of edge counts across the 93 used networks.

Results

Fitting multilevel ERGMs to Bipartite Networks

We encountered two issues worth highlighting.

  1. Network-size heterogeneity plays a vital role in convergence.

    The presence of a relatively large network negatively impacted convergence. As a response, we followed a two-step approach:

    1. Fit the model without the outlier graph.
    2. Use the estimates of that fit as a starting point for re-estimating the model, including the outlier network.

    The inclusion/exclusion of the outlier did not significantly affect the parameter estimates.

  2. Even in pooled models where network size heterogeneity could help, we experienced high collinearity between two-stars, concurrency, and geometrically weighted dyad-wise shared partners.1

Our strategy was to fit separate models featuring each of these terms and keep the one that resulted in the smallest AIC/BIC.

Model fit

  • The GWDSP effect is significantly negative, indicating a low chance of HCW overlapping residents.

  • Residents under wound care/bedridden have more HCWs associated with them than other patients.

  • Resident-homophily: Residents share HCWs with others with the same care needs.

  • Residents under ventilator care cluster around the same HCW.

  • Observing two or more of the same type of HCW serving the same resident is less likely than expected by chance.

  • No cohorting effect was observed among MDRO patients.

Table 2: Multilevel bi-partite ERGM fit with 93 networks.
Term Estimate
Structural terms
edges 3.58 \; (0.14)^{***}
log(n) \times edges -1.11 \; (0.04)^{***}
GWDSP (HCW centered) (decay = 0.75) -1.02 \; (0.04)^{***}
Nodal effects
Resident under wound care (yes/no) 0.16 \; (0.04)^{***}
Resident is bedridden (yes/no) 0.20 \; (0.05)^{***}
HCW centered 2-star mix
None with ventilator 0.01 \; (<0.01)^{***}
Both with ventilator 0.02 \; (0.01)^{*\hphantom{**}}
None with diabetes 0.04 \; (<0.01)^{***}
Both with diabetes 0.05 \; (0.01)^{***}
Resident centered 2-star mix
None nurse -0.11 \; (0.02)^{***}
Both nurse -0.37 \; (0.05)^{***}
None therapist 0.11 \; (0.01)^{***}
Both therapists -0.25 \; (0.10)^{*\hphantom{**}}
AIC 31,167.55
BIC 31,275.30
Log Likelihood -15,570.78

Discussion

  • Most network applications in healthcare focus on uni-partite networks (projections), e.g., physician-physician networks.

  • Leveraging recent advances in multi-network inference, we present one of the first applications of pooled bipartite ERGMs.

  • We found that

    1. Residents under wound care/bedridden have more HCWs associated with them than other patients.
    2. Residents share HCWs with others with the same care needs (ventilator and wound care).
    3. HCW assortativity (e.g., two nurses for the same resident) is less likely than expected by chance.
    4. We found no evidence of cohorting among MDRO patients.

  • Although cohorting is a common practice1, measuring its effectiveness is challenging, especially in endemic situations(Abad, Barker, and Safdar 2020).

  • We can leverage information about network structure to design other studies, e.g., agent-based models.

  • Future work will focus on the dynamics of these networks (using temporal ERGMs) and how they relate to pathogen transmission.

Appendix

Data: Interviews

  • HCPs working in the study unit were asked about their resident interactions between consecutive interviews about once every 60 to 90 minutes.

  • They were assigned a non-identifiable study ID that was used throughout the shift to permit the linkage of multiple interviews from the same HCP.

  • New IDs were given to all HCPs involved in the second round of interviews, making it implausible to associate first and second-round interviews.

Data: Resident Data

  • We collected standard patient demographics such as age, sex, race, and ethnicity.

  • We performed chart reviews for all residents in the two study units during the Epicenter data collection visits.

  • The data abstracted included:

    • Whether the patient was admitted for a short stay,
    • Had diabetes,
    • Was receiving dialysis,
    • Was bedridden,
    • Had urinary or central line catheters,
    • Had percutaneous gastrostomy/jejunostomy tube,
    • Was on a ventilator,
    • Had pressure ulcers, or
    • Was receiving wound care.

  • We also collected data on the presence of infections and any treatments prescribed for possible infections.

  • More information about the data collection process can be found in Nelson Chang et al. (2023).

  • Using the interview data, we built bipartite networks connecting HCW with residents.

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What drives resident-healthcare worker networks? – https://ggv.cl/slides/mind-june2024

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